Preheat oven to 350°. Sprinkle chicken with 2 teaspoons Cajun seasoning.
In a 12-inch cast-iron skillet, heat oil over medium-high heat. When oil is hot, reduce heat to medium. Working in batches, add chicken to skillet; cook, turning occasionally, until browned, about 6 minutes. Remove from skillet.
Add onion to skillet; cook, stirring occasionally, until lightly browned, about 5 minutes. Add rice and garlic; cook for 2 minutes. Add broth, lime juice, and remaining ½ teaspoon Cajun seasoning. Bring to a boil over medium-high heat. Boil for 8 minutes. Remove from heat; arrange chicken in rice mixture. Cover with foil.
Bake, until rice is tender and a meat thermometer inserted in thickest portion of chicken registers 165°, about 35 minutes. Remove from oven and let stand, covered, for 10 minutes. Garnish with lime wedges and cilantro, if desired.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/zesty-lime-chicken-rice/